Interatomic PotenRals in LAMMPS Aidan P. Thompson Sandia Na ...

Interatomic Poten-als in LAMMPS
Aidan P. Thompson
Sandia Na1onal Laboratories
2 nd LAMMPS Users Workshop
August 2011, Albuquerque, New Mexico
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,
for the United States Department of Energys National Nuclear Security Administration
under contract DE-AC04-94AL85000."

Recently Added Poten-als
• COMB poten-al (Genera-on 2)
Tzu-­‐Ray Shan (U Florida), talk on Tues PM metal and
semiconductors and their oxides
• Embedded ion method poten-als (EIM)
Xiaowang Zhou (Sandia), ionic compounds combo of Li,
Na, K, Rb, Cs, F, Cl, Br, and I
• C++ version of ReaxFF
Me1n Aktulga (LBNL), talk on Wed PM can be faster
than Fortran version by 2-­‐3x
• Electron force field (eFF)
Andres Jaramillo (Caltech), explicit electron dynamics in
extreme condi1ons

Recently Added Poten-als
• AIREBO poten-al bug fixes
Marcel Fallet & Steve Stuart (Clemson), one more bug-­fix,
upgrade is imminent
• Mishin ADP poten-al
Chris Weinberger (Sandia) & Chandra Veer Singh
(Cornell) angular-­‐dependent EAM for metals and alloys
• Dreiding poten-al
Tod Pascal (Caltech) hydrogen bonding for solvated bio-­molecules
• New Peridynamics poten-als
Mike Parks & Stuart Silling (Sandia), talk on Wed PM
fracture at the meso and con1nuum scales

Upcoming Poten-als
• Core/shell poten-al
Mike Chandross (Sandia), zero-­‐order model for polariza1on,
uranium and other nuclear fuel materials
• COMB poten-al (Genera-on 3)
Tzu-­‐Ray Shan (U Florida), more materials with polariza1on
effects
• MGPT poten-al
from John Moriarty & Jaime Marian (LLNL), tantalum and
other transi1on metals
• BOP poten-al
Xiaowang Zhou and Don Ward (Sandia) High-­‐accuracy
poten1al for semiconductors

LAMMPS Poten-al benchmarks

Compute Cost of Interatomic Poten-als
Growing Exponen-ally
Compute cost of LAMMPS poten1als
versus publica1on date
Cost [core-sec/atom-timestep]
10 -2
10 -3
10 -4
10 -5
10 -6
MEAM
CHARMm
Stillinger-Weber
EAM
Tersoff
EIM
ReaxFF
ReaxFF/C
AIREBO
h`p://lammps.sandia.gov/bench.html#poten1als
eFF
COMB
GAP
(Estim.)
1980 1990 2000 2010
Year Published
Drivers
• Cycles are cheap
• Availability of quantum
calcula1ons (N < 100)
• Qualita1ve accuracy no longer
enough

Challenges with Complex Poten-als
• How to Implement in LAMMPS?
– Rewrite code from scratch (REBO)
– Integrate exis1ng serial code (ReaxFF)
– Access via general API (KIM)
• How to Validate LAMMPS Version?
• How to Handle New Versions?

How to Fit Poten-als to New Materials?
• Automated fieng procedures exist for certain classes of
materials and poten1als (EAM)
• More commonly, good fits can be obtained only by gurus
(Baskes, van Duin)
• Combina1on of nonlinear op1miza1on and physical intui1on
• Increasing interest in automated machine-­‐learning
approaches
– Splines
– Gene1c programs
– Mul1-­‐objec1ve op1miza1on
– Neural networks
– Series expansions

GAP Approach for Interatomic Poten-als
GAP: A systema-c, informa-cs approach
• Based on QM and mathema1cs rather than
empiricism.
• Local density around each atom expanded in
4D hyperspherical harmonics, analogous to
Fourier series
• Atomic configura1ons described by
bispectrum of lowest-­‐order coefficients in
series
• Preserves universal physical symmetries:
invariance w.r.t. rota1on, transla1on,
permuta1on
• Gaussian process (GP) regression used to
interpolate energy of QM configura1ons
• 100-­‐1000x more expensive than MEAM
• Far cheaper than QM, linear scaling
• Can trade performance and accuracy
r
r cut
( ) = c j !
! r
j=0 m !,m=" j
m ,m Y j !
( )
m ,m
",#,$
Diamond: Force errors for GAP fi`ed to DFT.
Adding higher-­‐order GAP coefficients
systema1cally increases accuracy
Bartok et al., PRL 104 136403 (2010)
$
#
j
#

GAP Poten-al for Beryllium
Beryllium
Working with GAP developers, fieng directly
to forces and energies from high-­‐temperature
DFT MD simula1ons of small systems (from
Mike Desjarlais, 1640)
GAP Forces versus DFT Forces for
Liquid Be at 5,000 K, 250 atoms
!"
#$
#"
$
"
Temperature [K]
6000
5000
4000
3000
2000
Temperature [K]
6000
5000
4000
3000
2000
1000
Dr09 a-axis
Ba09i a-axis
DFT
DFT Melt Line
EOS Benedict et al.
Dr09 a-axis
Ba09i a-axis
DFT
0 DFT Melt Line
0 EOS 50 Benedict et 100 al. 150 200 250 300
P zz
[GPa]
!$
!#"
!#$
!!" !#$ !#" !$ " $ #" #$ !"
• Ini1al fit to:
− ambient HCP
− high-­‐pressure BCC and liquid
• Accurately reproduced that data
• Problems with:
− ambient elas1c constants
− high-­‐pressure HCP
• Need to refit with more data